Question

Write the negation of each of the following statements in two different ways.

(i) Africa is a continent.

(ii) $\sqrt{5}$ is rational.

(iii) All integers are rational numbers.

(iv) Some prime numbers are odd numbers.

(v) Everyone in Germany speaks German.

Answer 1

Given below are the required negations:

(i) Africa is not a continent. Or, It is false that Africa is a continent.

(ii) $\sqrt{5}$ is not rational.

Or, It is false that $\sqrt{5}$ is rational.

(iii) There exists an integer which is not a rational number.

Or, It is false that all integers are rational numbers.

(iv) No prime number is an odd number.

Or, It is false that some prime numbers are odd numbers.

(v) At least one person in Germany does not speak German.

Or, It is false that everyone in Germany speaks German.